1. Field of the Invention
The invention relates to a method and an arrangement for forming a secret communication key for a predetermined asymmetric key pair.
2. Description of the Related Art
The formation of an asymmetric cryptographic key pair is known from C. Ruland, Informationssicherheit in Datennetzen, ISBN 3-89238-081-3, DATACOM-Verlag, page 79–85, 1993 (Ruland I), which discloses the RSA method for forming a cryptographic key pair, which comprises a secret (private) key and a corresponding public key. Only the user knows the private key, but the public key can be made known to all subscribers of a communication network. In this method, the user signs the data with his private key when a digital signature is prepared for protecting the authenticity and integrity of electronic data. The signed digital signature is verified upon utilization of the public key corresponding to the private key, so that the authenticity or integrity of the digital signature can be checked by all communication partners, who have access to the public key. The previously mentioned “Public-Key-Technology” is particularly applied in the digital communication within a computer network (a fixed number of computer units, which are connected to one another via a communication network). Given the method known from Ruland, the protection of the private key against unauthorized access of a third party is of critical importance for the security of the digital signature.
It is known from D. Longley and M. Shain, Data & Computer Security, Dictionary of standards concepts and terms, Stockton Press, ISBN 0-333-42935-4, page 317, 1987 (Longley) to store the private key on an external medium for storing data, for example, a chip card, a disk etc., or on a hard disk, where key data are protected in that a personal identification code (Personal Identification Number, PIN) or a password, with which the key data that are respectively deciphered is used. It is necessary, however, to access the local resources of a user when these external media are used. This is not desired especially with respect to a network-oriented infrastructure of network computers or Java applications. These are defined as follows. A network computer is a computer that is networked with other computers; and a Java application is a program containing programs that are written in the programming language Java. The method known from Longley is disadvantageous in that the private key must be stored on an external medium, so that it is very difficult to protect the private key against misuse.
An overview regarding hash functions can be found in C. Ruland, Informationssicherheit in Datennetzen, ISBN 3-89238-081-3, DATACOM-Verlag, page 68–73, 1993 (Ruland II). A hash function is a function in which it is possible to calculate a corresponding input value to a given function value. Furthermore, an output character string having a fixed length is allocated to an arbitrarily long input character string. Moreover, additional properties can be requested for the hash function, such as collision freedom, which precludes the possibility of finding two different input character strings resulting in the same output character string. Examples of a hash function are the method according to the MD-2 standard, the method according to the MD-5 standard, the Data Encryption Standard (DES), which is carried out without utilizing a key, or any other arbitrary hash function.
A method referred to as a “Miller-Rabin” can determine whether a number is prime or not. Such a method is known from A. J. Menezes, P. van Oorschot and S. Vanstone, Handbook of Applied Cryptography, CRC Press, ISBN 0-8493-8523-7, page 138–140, 1997 (Menezes).